Plane adjustment (PA) is crucial for many 3D applications, involving simultaneous pose estimation and plane recovery. Despite recent advancements, it remains a challenging problem in the realm of multi-view point cloud registration. Current state-of-the-art methods can achieve globally optimal convergence only with good initialization. Furthermore, their high time complexity renders them impractical for large-scale problems. To address these challenges, we first exploit a novel optimization strategy termed \textit{Bi-Convex Relaxation}, which decouples the original problem into two simpler sub-problems, reformulates each sub-problem using a convex relaxation technique, and alternately solves each one until the original problem converges. Building on this strategy, we propose two algorithmic variants for solving the plane adjustment problem, namely \textit{GlobalPointer} and \textit{GlobalPointer++}, based on point-to-plane and plane-to-plane errors, respectively. Extensive experiments on both synthetic and real datasets demonstrate that our method can perform large-scale plane adjustment with linear time complexity, larger convergence region, and robustness to poor initialization, while achieving similar accuracy as prior methods. The code is available at https://github.com/wu-cvgl/GlobalPointer.

翻译：平面调整（Plane Adjustment, PA）对许多三维应用至关重要，涉及同时进行位姿估计与平面恢复。尽管近期取得进展，它仍是多视角点云配准领域中的一个挑战性问题。当前最先进的方法仅能在良好初始化的前提下实现全局最优收敛。此外，其较高的时间复杂度使其难以应用于大规模问题。为应对这些挑战，我们首先提出一种称为“双凸松弛”的新型优化策略：该策略将原问题解耦为两个更简单的子问题，利用凸松弛技术重构每个子问题，并交替求解直至原问题收敛。基于此策略，我们分别针对点对面误差与面对面误差，提出了两种求解平面调整问题的算法变体，即 GlobalPointer 与 GlobalPointer++。在合成与真实数据集上的大量实验表明，本方法能够以线性时间复杂度执行大规模平面调整，具有更大的收敛区域、对较差初始化的鲁棒性，同时达到与现有方法相当的精度。代码发布于 https://github.com/wu-cvgl/GlobalPointer。